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At least 523 records · Page 29

Application of numerical methods to extend capabilities for optimal rocket guidance: report on reentry guidance of shuttle orbiter

Analytical models are presented for optimal trajectories and reentry guidance of the space shuttle orbiter. Major emphasis is placed on the development of a "footprint', which refers to a set of reachable destination positions attainable by the shuttle at a specified terminal altitude. An unconstrained reentry footprint was calculated for a shuttle vehicle which enters the earth's atmosphere at 93 km initial altitude after a deboost from a near earth orbit. The method of computation is briefly described, and graphs are presented which illustrate the footprint and the variation of state and control variables along it. The effects of constraints and of variations in initial state upon the footprint are discussed.

Source record↗

Polarizabilities of two-electron positive ions and Rydberg levels of lithium

Second-order sums are computed for the two-electron positive ions Li(+), Be(2+), and B(3+) by representing the intermediate states as discrete pseudostates. The Hamiltonian for the system is given and translated to semi-Jacobi variables for its derivation in reduced Rydberg units. The interaction potential is developed in its multipole form and employed in second-order perturbation theory. The perturbation is always a multipole-potential term, and the initial and intermediate states are constructed from two-particle Hylleraas basis sets. The resulting pseudostates are shown to represent the continuum with good convergence, and the asymptotic-optical-potential method is applied to the two-body quantities to determine the energy levels of three-electron systems in high Rydberg states. The method is shown to give accurate values for the polarizabilities of the two-electron isoelectronic systems.

Bhatia, A. K.↗

Ab Initio Electronic Structure Calculations of CNN for CN Excitation Studies

The CN molecule is an important contributor to radiative heat flux in shock layers around vehicles entering Titan’s atmosphere. Current data for heavy particle (de)excitation rate coefficients of CN leads to uncertainties in the population of CN in its first and second excited states. This in turn leads to uncertainties in the radiative heat flux predicted by Computational Fluid Dynamics (CFD) simulations of Titan atmospheric entry. This work performs ab initio electronic structure calculations of the CNN complex to create Potential Energy Surfaces (PESs) that correlate to the ground and first and second excited states of CN. Specifically, the state combinations of CN(X,A,B) + N(4S𝑜) correlate to six states of CNN (three Quintet A” and three Triplet A”). Initial calculations of these states suggest that heavy particle (de)excitation of CN by N atoms is likely to proceed through collinear geometries on triplet surfaces. Complete PESs will show all of the reaction pathways in detail, and will be used in nonadiabatic dynamics calculations to evaluate improved rate coefficients and reduce uncertainty in the radiative heat flux during Titan entry.

Eric C Geistfeld↗

Ab Initio Electronic Structure Calculations of CNN for CN Excitation Studies

The CN molecule is an important contributor to radiative heat flux in shock layers around vehicles entering Titan’s atmosphere. Current data for heavy particle (de)excitation rate coefficients of CN leads to uncertainties in the population of CN in its first and second excited states. This in turn leads to uncertainties in the radiative heat flux predicted by Computational Fluid Dynamics (CFD) simulations of Titan atmospheric entry. This work performs ab initio electronic structure calculations of the CNN complex to create Potential Energy Surfaces (PESs) that correlate to the ground and first and second excited states of CN. Specifically, the state combinations of CN(X,A,B) + N(4S𝑜) correlate to six states of CNN (three Quintet A” and three Triplet A”). Initial calculations of these states suggest that heavy particle (de)excitation of CN by N atoms is likely to proceed through collinear geometries on triplet surfaces. Complete PESs will show all of the reaction pathways in detail, and will be used in nonadiabatic dynamics calculations to evaluate improved rate coefficients and reduce uncertainty in the radiative heat flux during Titan entry.

Eric Geistfeld↗

Large Eddy Simulation of Homogeneous Rotating Turbulence

Study of turbulent flows in rotating reference frames has proven to be one of the more challenging areas of turbulence research. The large number of theoretical, experimental, and computational studies performed over the years have demonstrated that the effect of solid-body rotation on turbulent flows is subtle and remains exceedingly difficult to predict. Because of the complexities associated with non-homogeneous turbulence, it is worthwhile to examine the effect of steady system rotation on the evolution of an initially isotropic turbulent flow. The assumption of statistical homogeneity considerably simplifies analysis and computation; calculation of homogeneous turbulence is further motivated since it possesses the essential physics found in more complex rotating flows. The principal objectives of the present study have therefore been to increase our fundamental understanding of turbulent flows in rotating reference frames through an examination of the asymptotic state of homogeneous rotating turbulence; particularly as to the existence of an asymptotic state which is self similar. Knowledge of an asymptotic similarity state permits prediction of the ultimate statistical evolution of the flow without requiring detailed knowledge of the complex, and not well understood, non-linear transfer processes. Aside from examination of possible similarity states in rotating turbulence, of further interest in this study has been an examination of the degree to which solid-body rotation induces a two-dimensional state in an initially isotropic flow.

Squires, Kyle D.↗

A fast viscous correction method for unsteady transonic flow about airfoils

This study modified the inviscid, small-disturbances, unsteady, transonic code, LTRAN2, so that the viscous effect could be considered for the purpose of improving the code's accuracy without substantially increasing the computational time. By using a conventional integral boundary layer method to determine the displacement thickness and an empirical model of viscous wedge to simulate the suddenly thickened boundary layer behind a shock, it resulted in better agreement with experimental data for both the shock position and the pressure coefficient. Aerodynamic performances were calculated for two supercritical airfoils. When the unsteady procedure was used to obtain steady state results as the initial condition, the unsteady viscous solution for the RAE 2822 airfoil required 100.5% of the computational time of the inviscid solution. When an iterative scheme was used to obtain the steady state results as the initial condition, the unsteady viscous solution for the NLR 7301 airfoil required 88% of the computational time of the inviscid solution.

Lee, S. C.↗

Improved Benchmarking of Cohesive Elements in Abaqus Standard for Predicting Disbond and Delamination in Composite Structures

Traditional approaches for aircraft certification require the assumption of an initial flaw condition, either represented as barely visible impact damage (BVID) or through inclusion of a Teflon insert to serve as surrogate damage. Based on the initial composite damage state, the structure must be shown to demonstrate structural durability and damage tolerance (DaDT) according to the following criteria: a. Damage displays no detrimental growth under cyclic loading b. The structure is able to sustain design limit load (DLL) Currently, the only available manner for validating structural performance is through test. Since damage can occur over a wide variety of areas within a structure, this approach has proven to be increasingly expensive and time consuming for composite airframes and acreage structure within the design-test-certification building block. A further complicating factor is the requirement to accurately capture the most critical damage morphologies as a starting condition. To understand the severity of the damage, it is either required to experimentally determine the most critical areas at tremendous expense or rely on legacy data of similar structural testing, which limits design space expansion. A preferred solution is to use advanced analysis to provide improved understanding of load margins for critical locations based on a wide variety of potential starting damage conditions. The standard industry approach for DaDT certification adheres to the use of the traditional virtual crack closure technique (VCCT) method. VCCT is generally a preferred method because it conforms to the current certification principles of damage from a known flaw, and when used correctly, can be effective at predicting delamination propagation under static and cyclic loading. The VCCT method requires the inclusion of an initial flaw in the finite element (FE) model requiring a-priori knowledge of the flaw location. This in turn requires a plethora of analysis cases to be examined to cover a reasonable span of potential damage states. Additionally, the VCCT approach requires node-to-node connectivity rendering it incompatible with the best practices and approaches for using continuum damage mechanics (CDM) based progressive damage and failure analysis (PDFA) tools within a typical FE solver. Alternatives to VCCT have emerged in the form of cohesive elements which utilize the cohesive zone model (CZM). Unlike VCCT which models linear elastic fracture mechanics, cohesive elements couples continuum and fracture based responses through the use of bilinear traction separation laws. These laws are defined based on a penalty stiffness, a cohesive strength, and a strain energy release rate. The approach can be mesh regularized with native cohesive elements within many FE solvers such as Abaqus and LS-DYNA. In Phase I of the NASA Advanced Composites Consortium (ACC) post-buckled stiffened panel with BVID, Strength and Life [1], the performance of cohesive elements were benchmarked in comparison to VCCT and LEFM solutions and showed good agreement using Abaqus explicit [2]. To realize savings on current and future programs, it is still necessary to close technical gaps related to the use of cohesive elements with Abaqus Standard. Within a program environment, standard finite element analysis is the preferred analytical capability for quasi-static loading as it eliminates uncertainty due to oscillatory behavior commonly seen with explicit analysis. This oscillatory behavior creates difficulties in writing margins of safety based on the analysis. The use of negative tangent stiffness material models complicates convergence which typically requires the use of numerical controls such as viscous damping to overcome. To date, there has not been a comprehensive study on how to establish best practices for cohesive element convergence for predictive capability within the Abaqus implicit solver. In pursuit of these goals, under the NASA ACC program, several numerical benchmark problems were proposed including pure mode I (double cantilevered beam – DCB), pure mode II (end notch flexure – ENF), and symmetric/unsymmetric evolving mixed mode (single leg bend – SLB). This paper focuses on the use of cohesive elements to model the delamination through the use of CZM. Specifically, finite element models for the DCB, ENF, symmetric SLB, and unsymmetric SLB, are developed and various solution controls for convergence are studied to develop a best practice. Once the best practice has been developed, the predictive capability of the objective CZM model is used to analyze the hat pull-off strength of a standard hat stiffened configuration under various loading conditions.

Abaqus↗

A numerical study of the nonlinear thermal stability of solar loops

A time-dependent numerical model is used to investigate the nonlinear thermal stability of static loops of various heights. Simulations show that the instability of a hot state with loop heights of less than about 1000 km is physically significant, with an initially hot atmosphere in low-lying compact loops evolving to an extended atmosphere with temperatures far below 100,000 K. Results also show that high-lying loops are stable to all reasonable perturbations, including those of large initial amplitude and long wavelength. The simulation results suggest that low-lying compact loops should not be common to the sun, and that cool loops with temperatures near 100,000 K must be formed in the cool state initially and cannot evolve from preexisiting loops.

Klimchuk, J. A.↗

Theoretical Studies of N2-broadened Half-widths of H2O Lines Involving High j States

Based on the properties of the energy levels and wave functions of H2O states, one can categorize H2O lines into individually defined groups such that within the same group, the energy levels and the wave functions associated with two paired lines have an identity property while those associated with different pairs have a similarity property. Meanwhile, by thoroughly analyzing processes used to calculate N2-broadened half-widths, it was found that the 'Fourier series' of W(sup a)(sub L(sub 1))(sub K(sub 1))(sub K(sub 1)) (t; j(sub f) T(sub f) and W(sup a)(sub L(sub 1))(sub K(sub 1))(sub K(sub 1)) (t; j(sub i) T(sub i), and a factor P(sub 222) (j(sub f) T(sub f) j(sub i) T(sub i)) are the key items in the Robert-Bonamy formalism to distinguish contributions to ReS2(r(sub c)) among different transitions of j(sub f) T(sub f) - j(sub i). However, these items are completely determined by the energy levels and the wave functions associated with their initial and final states and they must bear the latter's features as well. Thus, it becomes obvious that for two paired lines in the same group, their calculated half-widths must be almost identical and the values associated with different pairs must vary smoothly as their ji values vary. Thus, the pair identity and the smooth variation rules are established within individual groups of lines. One can use these rules to screen half-width data listed in HITRAN and to improve the data accuracies.

water↗

Meteoroid-bumper interactions program

An investigation has been made of the interaction of meteoroids with shielded structures. The interaction has been simulated by the impact of Lexan cylinders onto lead shields in order to provide the vaporous debris believed to be created by meteoroid impact on a space vehicle. Shock compression data for Lexan was determined. This, in combination with the known shock compression data for the lead shield, has permitted the definition of the initial high pressure states in the impacted projectile and shield. The debris from such impact events has been permitted to interact with aluminum main walls. The walls were chosen to be sufficiently large to be effectively infinite in diameter compared to the loaded area. The thickness of the wall and the spacing from the shield were varied to determine the effect of these parameters. In addition, the effect of having a body of water behind the wall has been assessed. Measurements of the stagnation pressure in the debris cloud have been made and correlated with the response of the main wall.

Gough, P. S.↗

Molecular collisions. XVI.

The comparison indicates that the present version of the GPS method overestimates the rotational excitation and underestimates the de-excitation, while maintaining the total inelasticity at approximately the correct exact classical trajectory value. An approximate ?quantization' of the classical results leads to an estimate of the quantal cross sections corresponding to changes by plus or minus 2, 4, and 6 from an initial rotor quantum state 10. It is found that most of the total inelastic cross section arises from the first-order-allowed transitions.

Pattengill, M. D.↗

An electron microscopy examination of primary recrystallization in TD-nickel.

Primary recrystallization in TD-nickel 1 in. bar has previously been regarded as the process by which the initial fine grain structure is converted to a coarse grain size (increases in grain size by 500 times) under suitable deformation and annealing conditions. This process is dependent on deformation mode. While it occurs readily after rolling transverse to the bar axis and annealing (800 C), it is completely inhibited by longitudinal rolling and swaging deformations, even for very high (1320 C) annealing temperatures. A transmission electron microscopy examination of deformation and annealing substructures indicates that primary recrystallization in TD-nickel 1 in. bar actually occurs on the sub-light optical level, to produce a grain structure similar in size to the initial fine grained state.

Petrovic, J. J.↗

Calculation of the total electron excitation cross section in the Born approximation using Slater wave functions for the Li (2s yields 2p), Li (2s yields 3p), Na (3s yields 4p), Mg (3p yields 4s), Ca (4s yields 4p) and K (4s yields 4p) excitations

Excitation of neutral atoms by inelastic scattering of incident electrons in gaseous nebulae were investigated using Slater Wave functions to describe the initial and final states of the atom. Total cross sections using the Born Approximation are calculated for: Li(2s yields 2p), Na(3s yields 4p), k(4s yields 4p). The intensity of emitted radiation from gaseous nebulae is also calculated, and Maxwell distribution is employed to average the kinetic energy of electrons.

Simsic, P. L.↗

On the passage of radiation through inhomogeneous, moving media. XII - Polarized waves in a plane, sheared medium

Using the complete set of Maxwell equations, the ray paths and Stokes parameters of a polarized wave are followed which passes through a slab of differentially shearing material of variable refractive index. The polarization state of the signal leaving the top of the slab is related to the polarization state of the initial wave. In general, the two are not the same. These calculations were made to illustrate the point that the polarization properties of observed pulsar signals may be very different from those of the emitted signals due to propagation effects in the differentially shearing magnetospheres that most pulsars are believed to possess. While it is recognized that the precise amount of polarization variations is model dependent, the calculations show that even for simple situations a noticeable polarization variation occurs. Accordingly, the calculations reported here are an educative device: they show that it is, perhaps, unwise to assume that the observed polarization properties of pulsar signals are the same as the emitted signals.

Lee, M. A.↗

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Cooke, C. H.↗

Theoretical L-shell Coster-Kronig energies 11 or equal to z or equal to 103

Relativistic relaxed-orbital calculations of L-shell Coster-Kronig transition energies have been performed for all possible transitions in atoms with atomic numbers. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order approximation to the local approximation was thus included. Quantum-electrodynamic corrections were made. Each transition energy was computed as the difference between results of separate self-consistent-field calculations for the initial, singly ionized state and the final two-hole state. The following quantities are listed: total transition energy, 'electric' (Dirac-Hartree-Fock-Slater) contribution, magnetic and retardation contributions, and contributions due to vacuum polarization and self energy.

Chen, M. H.↗

On-line parameter estimation using a high sensitivity estimator

An on-line parameter identification method is presented. The method is based on a recursive formulation of the maximum likelihood method, with a significant modification on the gains of the state estimator. In the conventional maximum likelihood method, the Kalman gains are used in the state estimator. This produces unbiased, minimum variance parameter estimates in the presence of process noise and measurement noise, but it also slows the convergence rate when the identification is done on-line. Here we suggest choosing the gains to maximize a measure of the sensitivities of the state estimates to parameter variations. One such criterion is to minimize the trace of the inverse information matrix. This increases the convergence rate significantly. After one or two time constants, the gains are switched to the Kalman values to assure unbiased, minimum-variance estimates. The state estimate will initially be nonoptimal, and may not be adequate for control purposes. In this case, a parallel Kalman filter which uses the identifier's parameter estimates can be used. This method is applied here for the identification of a simple first-order system, and for the identification of short-period stability derivatives of an F-8 aircraft from simulated data.

Mishne, D.↗